JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(\mathrm{z}\) be a complex number such that \(|\mathrm{z}+2|=1\) and \(\operatorname{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}\). Then the value of \(|\operatorname{Re}(\overline{z+2})|\) is :
- A \(\frac{\sqrt{6}}{5}\)
- B \(\frac{1+\sqrt{6}}{5}\)
- C \(\frac{24}{5}\)
- D \(\frac{2 \sqrt{6}}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \sqrt{6}}{5}\)
Step-by-step Solution
Detailed explanation
\( |z+2|=1, \operatorname{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5} \) \( \text { Let } z+2=\cos \theta+i \sin \theta \) \( \frac{1}{z+2}=\cos \theta-i \sin \theta \) \( \Rightarrow \frac{z+1}{z+2}=1-\frac{1}{z+2}=1-(\cos \theta-i \sin \theta) \)…
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